A manufacturing company produces cylindrical metal cans. The cans need to have a volume of $500\pi \text{ cm}^3$. The cost of the metal for the top and bottom of the can is \$0.02 \text{ cents/cm}^2$, and the cost of the metal for the curved side is \$0.01 \text{ cents/cm}^2$.
b. Find the value of $r$ that minimizes the cost of producing the can. Justify that this value of $r$ gives a minimum cost.
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Create Free Account Log inThis is a free VCE Units 3 & 4 Mathematical Methods practice question worth 4 marks, testing your understanding of Optimisation Problems. It falls under Calculus in Unit 3: Mathematical Methods Unit 3. Submit your answer above to receive instant AI-powered marking and personalised feedback.
Extend introductory study of functions, algebra, calculus. Focus on functions, relations, graphs, algebra, and applications of derivatives.
Covers limits, continuity, differentiability, differentiation, and anti-differentiation.
identification of local maximum/minimum values over an interval and application to solving optimisation problems in context, including identification of interval endpoint maximum and minimum values
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